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From a wikipedia article concerning Epigenetic research

Evolution
Although epigenetics in multicellular organisms is generally thought to be a mechanism involved in differentiation, with epigenetic patterns "reset" when organisms reproduce, there have been some observations of transgenerational epigenetic inheritance (e.g., the phenomenon of paramutation observed in maize). Although most of these multigenerational epigenetic traits are gradually lost over several generations, the possibility remains that multigenerational epigenetics could be another aspect to evolution and adaptation. These effects may require enhancements to the standard conceptual framework of the modern evolutionary synthesis.[32][33]
Epigenetic features may play a role in short-term adaptation of species by allowing for reversible phenotype variability. The modification of epigenetic features associated with a region of DNA allows organisms, on a multigenerational time scale, to switch between phenotypes that express and repress that particular gene.[34] When the DNA sequence of the region is not mutated, this change is reversible. It has also been speculated that organisms may take advantage of differential mutation rates associated with epigenetic features to control the mutation rates of particular genes.[34]


Transgenerational epigenetic observations
Marcus Pembrey and colleagues also observed that the paternal (but not maternal) grandsons of Swedish boys who were exposed during preadolescence to famine in the 19th century were less likely to die of cardiovascular disease; if food was plentiful then diabetes mortality in the grandchildren increased, suggesting that this was a transgenerational epigenetic inheritance.[40] The opposite effect was observed for females -- the paternal (but not maternal) granddaughters of women who experienced famine while in the womb (and their eggs were being formed) lived shorter lives on average.[41]

DNA methylation profiles in monozygotic and dizygotic twins
Zachary A Kaminsky1,2, Thomas Tang1, Sun-Chong Wang1,3, Carolyn Ptak1,2, Gabriel H T Oh1,2, Albert H C Wong1,2, Laura A Feldcamp1,2, Carl Virtanen4, Jonas Halfvarson5,6, Curt Tysk5,6, Allan F McRae7, Peter M Visscher7, Grant W Montgomery7, Irving I Gottesman8, Nicholas G Martin7 & Art Petronis1,2
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Twin studies have provided the basis for genetic and epidemiological studies in human complex traits1, 2. As epigenetic factors can contribute to phenotypic outcomes, we conducted a DNA methylation analysis in white blood cells (WBC), buccal epithelial cells and gut biopsies of 114 monozygotic (MZ) twins as well as WBC and buccal epithelial cells of 80 dizygotic (DZ) twins using 12K CpG island microarrays3, 4. Here we provide the first annotation of epigenetic metastability of 6,000 unique genomic regions in MZ twins. An intraclass correlation (ICC)-based comparison of matched MZ and DZ twins showed significantly higher epigenetic difference in buccal cells of DZ co-twins (P = 1.2 10-294). Although such higher epigenetic discordance in DZ twins can result from DNA sequence differences, our in silico SNP analyses and animal studies favor the hypothesis that it is due to epigenomic differences in the zygotes, suggesting that molecular mechanisms of heritability may not be limited to DNA sequence differences.